 | George Washington Hull - 1807 - 408 σελίδες
...they are similar to each other. PROPOSITION XVIII. THEOREM. 254. Two triangles are similar when they have an angle of one equal to an angle of the other, ancL the sides including these angles proportional. *BD* Given — The triangles ABC and DEF, with... | |
 | Adrien Marie Legendre - 1819 - 574 σελίδες
...of triangles involve those of all figures, THEOREM. 208. Two triangles, whkh Iiave an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Fig. 122. Demonstration. Let the angle A = D (Jig. 122), and... | |
 | Rev. John Allen - 1822 - 508 σελίδες
...FE, as FD to AC). And triangles (ABC, DEF), which have an angle (ACB) of one, equal to an angle (F) of the other, and the sides about the equal angles reciprocally proportional, are equal. Part 1.—On BC and AC produced, take CG equal to FE, CH to FD, and join AG and GH. The... | |
 | Rev. John Allen - 1822 - 516 σελίδες
...HG, and of PB to BL or HE. Cor. 1. — By a similar reasoning it may be proved, that triangles, which have an angle of one, equal to an angle of the other, are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles. Cor.... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...triangles DEF, ABC, are equiangular and similar. THEOREM 60. 158. Two triangles which have an angle of the one equal to an angle of the other, and the sides about them proportionals, are similar. Let the angle A equal D, and suppose that AB : DE : : AC : DF, the... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 σελίδες
...that AB : FG : : BC : GH. It follows from this, that the triangles ABC, FGH, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (208), consequently the angle BCA = GHF. These equal angles being subtracted... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A-=D (fig. 122), and let Fifr... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A = D (Jig. 122), and let Fig.... | |
 | Euclid - 1826 - 234 σελίδες
...equal angles are reciprocally proportional ; and if triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, these triangles are equal. BAC equal to an angle DAE ; then the sides of the triangles ABC, ADE, are... | |
 | Euclides - 1826 - 226 σελίδες
...angles are reciprocally proportional; and if parallelogram* h.ave one angle of the one equal to one angle of the other, and, the sides about the equal angles reciprocally proportional; these parallelograms shall be equal to one another. • I*-1- foreFB, вс,аге in a direct line... | |
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... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. 
